Consider filling the bottom of your shallow mug
with a puck of Williams or just melt some common
glycerin face soap when it gets empty. If the puck
of Williams is too much grate it down a bit....
My favorite mug, like yours is too deep and this
works for me. Since my mug is wide I put some glycerin
soap in it warmed it up to melt in the microwave
and then pushed a puck of Williams into the molten
glycerin soap and let it all cool.
When it cooled I dropped in a puck of higher end mug
soap with just enough water to let them glue together
after drying.
Right now I have a puck of Cyril R Salter Shaving Soap
on top and am loving it.